Download HW: Gravity practice

Newton’s Universal Law of Gravitation Practice
Mearth = 6.0 x 1024 kg
Rearth = 6.4 x 106 m
1. A 5.0 kg and a 10. kg sphere are 0.30 m apart (center-to-center distance). Find the force of
attraction between them.
2. An object weighs 100. N on the surface of the earth. Find its weight if it was 6.38 x 106 m
above the surface?
3. Calculate the acceleration due to gravity at a point 1000. km above the surface of the earth.
4. The force of gravity on a 60 kg woman is 588 N. The woman also exerts a gravitational force
on the Earth. How large a force is this?
5. The force of attraction between m1 and m2 is 26 N. What will this force become if m2 is tripled
and the distance between it and m1 is halved?
6. The force of gravity between two masses was 14 N when they were 10. m apart. The distance
between them was changed and the force became 56 N. How far apart were they then?
7. The force of gravity between A and B is 100. N. When the mass of B is doubled and the
distance between it and A is quadrupled, what is the new force?
8. If the moon’s mass were suddenly to double, what effect would this change have on the
moon’s orbit, and how would such a change affect the Earth? (Assume that the velocity of the
moon remains unchanged.)
9. What are the units of G in the MKS (m-kg-sec) system?
10. Calculate the gravitational attraction between a proton of mass 1.67 x 10-27 kg and an electron
of mass 9.11 x 10-31 kg if they are 5.0 x 10-11 m apart (as they are in a normal hydrogen atom).
11. Find the acceleration of a falling object on Mars, given that the radius of Mars is one-half that
of Earth and the mass of Mars is one-eighth that of Earth.
12. The planet Saturn has mass of 5.67 x 1026 kg and radius of 6.3 x 107 m. Find the acceleration
due to gravity on Saturn. How much will the gravitational force be on a 60. kg man there?
13. A woman standing on the surface of the Earth, 6.38 x 106 m from its center, has a mass of
50.0 kg. If the mass of the Earth is 5.98 x 1024 kg, what is the force of gravity on the woman?
14. The force of gravitational attraction between two masses is 36 N. What will be the force if one
mass is doubled and the distance between them is tripled?
15. The planet Jupiter has a mass of 1.9 x 1027 kg and a radius of 7.2 x 107 m. Calculate the
acceleration due to gravity on Jupiter.
16. It is known that g varies as we go down into a hole towards the center of the earth. The
variation is not inversely proportional to the square of the distance from the center. Why?
17. A person proceeds away from the earth. How do you expect his weight to vary and why?
18. A mass, of “M” kg, has a force of 50. N when “R” meters from another mass of “m” kg. What is
the force on the mass “M” when the distance is changed to
(a) R/2; (b) R/3; (c) R/10?
19. (a) What is the weight of a 1.0 kg mass one earth radius from the surface of the earth?
(b) At what distance from the surface is a man’s weight reduced to one-half its original value?
20. How many earth radii away from the surface of the earth must one be to have one’s weight
reduced to 1 percent of its value at the surface?
21. Calculate the gravitational force on the earth due to the sun. It is this force which holds the
earth in its orbit.
Mass Sun = 1.99 x 1030 kg
Mass Earth = 6. X 1024 kg
R = 1.5 x 1011 m
22. Sally (55 kg) and Jimmy (70. kg) have been rumored to be dating for weeks. Some say they
are “in love”, but others say that they are simply “attracted” to one another. What is the force of
attraction between these two, assuming that they sit 10. m apart (from center of gravity to center
of gravity) in class?
23. In deep, deep, deep, space, nothing exists. Suddenly, two masses appear, separated by a
short distance. One mass is twice the size of the other mass. Find the acceleration of the large
mass relative to the acceleration of the smaller mass.